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Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory

Published online by Cambridge University Press:  20 November 2018

Yoon Sung Hwangk  and
Bill Jacob
Yoon Sung Hwangk
Affiliation:
Korea University, Seoul136-701, Korea
Bill Jacob
Affiliation:
University of California-Santa Barbara, Santa Barbara, California 93106, U.S.A.
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Abstract

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Let F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.

Keywords

1216
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 3 , 01 June 1995 , pp. 527 - 543
Copyright
Copyright © Canadian Mathematical Society 1995

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